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Math puzzle.

  1. Sep 7, 2005 #1
    I have no idea...

    A man has three daughters. His friends want to know how many years old the daughters are. The man gives them a hint.

    HINT #1
    The product of their ages is 72.

    The friends say this is not enough information so the man gives them a second hint.

    HINT #2
    The sum of their ages is equal to my house number.

    The friends go out and look at his house number and tell the man that they still do not have enough information to determine the ages. The man admits that they need more clue and gives them a third hint.

    HINT #3
    The oldest of the girls likes strawbarry ice-cream.

    How old are the three girls??
  2. jcsd
  3. Sep 8, 2005 #2


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    3, 4 and 6
  4. Sep 8, 2005 #3
    how did u get there?
  5. Sep 8, 2005 #4


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    Assumed that the ages were integer values.

    Any age is a function of time. Since ages are changing with time, then as the questioner is posing his question his statement (the sum of their ages is 72) becomes out of date and no longer valid.

    The solution is impossible otherwise. It would seem to be a trick question possibly, in which a justification for the actions of the friends is simply that they are dumb-dumbs. !!
  6. Sep 8, 2005 #5
    What are the second and third hints for seriously!
  7. Sep 8, 2005 #6


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    The product of the three ages is 72. Find all ways to factor 72 into 3 integers.

    For example, 1, 1, 72; 1, 2, 36; 1, 3, 24;1, 4, 9; 1,6,12; etc.

    Obviously there are many different ways to do that. That's why "That's not enough information".

    Now we are told- "The sum of their ages is equal to my house number."

    Well,that makes it easy, doesn't it? Just add the three numbers in each set and see which add up to the house number!

    One problem: We don't know what the house number is! But the friends did. Why would they say again "that's not enough information"??

    Perhaps because more that one of the triples added to the house number?

    We still don't know what that house number is- but perhaps only two sets of the three ages add to the same number! Add them up and see!

    Finally "The oldest of the girls likes strawbarry ice-cream."

    Clearly the "strawberry ice-cream" is not important. What is important is that there is an oldest girl! Once you have found all ways of factoring 72 into 3 integers and added each set of 3 you will see what I mean. Do It!

    However, I do not get "3, 4, and 6". I get 3, 3, and 8.
    Last edited by a moderator: Sep 8, 2005
  8. Sep 8, 2005 #7
    Thank you.
  9. Sep 8, 2005 #8


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    Wow, that was clever HallsofIvy. :surprised
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